The SDRI model of [1]} is a variational model introduced in the framework of the SDRI theory initiated in the seminal papers of [2]} and [3]}, and on the basis of the subsequent analytical descriptions provided in the context of epitaxially strained thin films [4]}, [5]}, [6]}, [7]}, crystal cavities [8]}, [9]}, capillarity droplets [10]}, [11]}, fractures
[12]}, [13]}, [14]}, [15]}, [16]}, and boundary debonding and delamination [17]}, [18]}. All such settings are included and can be treated simultaneously in the SDRI model [1]} (see Section REF ). In agreement with [2]}, [3]} since SDRI morphologies relate to the boundary of crystalline materials and depend on the bulk rearrangements, the energy \(\mathcal {F}\)  characterizing the SDRI model displays both an elastic bulk energy and a surface energy denoted by \(\mathcal {W}\)  and \(\mathcal {S}\) , respectively. More precisely, the energy \(\mathcal {F}\)  is defined as
\(\mathcal {F}(A,u):=\mathcal {S}(A,u) + \mathcal {W}(A,u)\) 
